Having reviewed the essential RG, let us now discuss
the criteria of asymptotic safety as formulated by Weinberg [1]} and how it is realised by solving the flow equation for the EAA within an essential scheme. The criteria necessitate that we have a UV-complete QFT where there is no UV cut-off, which is achieved if the theory lies on an RG trajectory that originates from a UV fixed point. However, as has been emphasised recently [2]}, Weinberg's formulation is more precise since it is concentrated on the absence of unphysical UV divergences in physical quantities, such as reaction rates, rather than on the behaviour of correlation functions of fields \(\hat{\phi }\) . This is important since correlation functions depend on inessential couplings \(\zeta _\alpha \) . In a scheme where we do not specify the values of inessential couplings but compute their flow, we are at the very least making our life harder unnecessarily. In the worst-case, an inessential coupling may not reach a fixed point and thus in such a scheme asymptotic safety could be obscured. In an essential scheme, we only compute the flow of the essential couplings and, thus, avoid these matters.
